Question

If one of the roots of $\begin{vmatrix} 3 &5 & x \\\ 7 & x & 7 \\\ x & 5 & 3 \end{vmatrix} = 0$ is -10,then the other roots are

• A. 44627
• B. 4 , 7
• C. 44629
• D. 3,4

Answer 1

Answer: (A)

44627

Answer 2

Given, $\begin{vmatrix} 3 &5 & x \\\ 7 & x & 7 \\\ x & 5 & 3 \end{vmatrix} = 0$
$\Rightarrow \ \ \ 3(3x - 35) - 5(21 - 7x) + x(35 - x^2) = 0$
$\Rightarrow \ \ \ 9x - 105 - 105 + 35x + 35x - x^3 = 0$
$\Rightarrow \ \ \ x^3 - 79x + 210 = 0$
$\Rightarrow \ \ \ (x + 10) (x - 3) (x -7) = 0$
$\Rightarrow \ \ \ x = -10, 3, 7$